Question

In a triangle ABC, the lengths of sides AB and BC are 18 cm and 40 cm respectively. If the angle between these two sides is 90 degrees, the area of the triangle is

• A. 350 sq.cm
• B. 380 sq.cm
• C. 390 sq.cm
• D. 360 sq.cm

Hint:

For right-angled triangles, the area is simply half of the product of the two shorter sides. \[ \text{Area} = \frac{18 \times 40}{2} = 360 \]

Answer 1

The Correct Option is D

Concept: When a triangle has an angle of 90 degrees (a right-angled triangle), the two sides forming that angle are the "base" and the "height" of the triangle. The formula for the area is: \[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]

Step 1: Identify Base and Height.
We are given that $\angle ABC = 90^\circ$. Therefore, sides $AB$ and $BC$ are perpendicular to each other. Base ($b$) = 40 cm
Height ($h$) = 18 cm

Step 2: Apply the Area Formula.
Substitute the dimensions into the area formula: \[ \text{Area} = \frac{1}{2} \times 40 \times 18 \]

Step 3: Perform the final calculation.
Simplify the expression: \[ \text{Area} = 20 \times 18 \] \[ \text{Area} = 360 \] The area of the triangle $ABC$ is 360 square centimeters. Final Answer: Option D